Physics 1240: Sound and Music · Physics 1240: Sound and Music. Today (7/25/19): Vibrating Air Columns, Organs. Next time: Woodwinds, Brass Instruments

Physics 1240: Sound and Music

Today (7/25/19): Vibrating Air Columns, Organs

Next time: Woodwinds, Brass Instruments

Student performance:flute

Review

Types of Instruments(Hornbostel–Sachs classification)

• Chordophones: vibrating strings

• Aerophones: vibrating columns of air

• Idiophones: vibrating the whole instrument

• Membranophones: vibrating membrane/skin

• Electrophones: vibrating loudspeaker

Review

Chordophones

• Zithers

• Lutes

• Harps

• How to create waves: initial displacement, velocity, or both

𝑓𝑓𝑛𝑛 =𝑛𝑛2𝐿𝐿

𝑇𝑇𝑚𝑚/𝐿𝐿

Clicker Question 12.1

If you pluck a string at its halfway point, which of the first five harmonics will be present?

A) 1, 3, 4, 5B) 1, 3, 5C) 1D) 2, 4E) 1, 2, 3, 4, 5

BA


If you pluck a string at its halfway point, which of the first five harmonics will be present?

A) 1, 3, 4, 5B) 1, 3, 5C) 1D) 2, 4E) 1, 2, 3, 4, 5

BA

1st

2nd

3rd

4th

5th


If the string on a grand piano for the note that plays middle C is 4 feet long, how long would the string for the lowest C (three octaves down) need to be if no changes are made to the string’s tension or gauge?

A) 0.5 ftB) 4 ftC) 8 ftD) 16 ftE) 32 ft

BA


If the string on a grand piano for the note that plays middle C is 4 feet long, how long would the string for the lowest C (three octaves down) need to be if no changes are made to the string’s tension or gauge?

A) 0.5 ftB) 4 ftC) 8 ftD) 16 ftE) 32 ft

BA

𝑓𝑓𝑛𝑛 =𝑛𝑛2𝐿𝐿

𝑇𝑇𝑚𝑚/𝐿𝐿

If 𝑓𝑓 goes down three octaves (decreases by a factor of 23=8), 𝐿𝐿 must increase by a factor of 8

Aerophones: vibrating columns of air

What happens when air gets to the edge of a pipe?(for a string, it reflects and becomes upside-down)


• Closed end: wave pulse reflects in a normal way


• Open end: wave pulse reflects and inverts

λ = 4𝐿𝐿 λ = 2𝐿𝐿


• Standing waves:What do we plot so we don’t have to draw longitudinal waves with air molecules?

1st harmonic

2nd harmonic

3rd harmonic


• Standing waves:

• Two choices:1. Velocity/Displacement2. Pressure

• Closed end:velocity node,pressure antinode

• Open end:velocity antinode,pressure node


For a pipe open at both ends, what quantity has a node at the open ends?

A) PressureB) VelocityC) None of the above

BA

1st harmonic

2nd harmonic

3rd harmonic


• Open pipe:

Velocity Pressure

𝐿𝐿 =λ2

𝐿𝐿 = λ

𝐿𝐿 =3λ2

𝐿𝐿 = 2λ

1st harmonic

2nd harmonic

3rd harmonic

4th harmonic

𝐿𝐿 =𝑛𝑛𝜆𝜆2

𝑓𝑓𝑛𝑛 = 𝑛𝑛𝑣𝑣2𝐿𝐿


• Closed pipe:

Velocity Pressure

𝐿𝐿 =λ4

𝐿𝐿 =3λ4

𝐿𝐿 =5λ4

1st harmonic

(no 2nd harmonic)

3rd harmonic

(no 4th harmonic)

𝐿𝐿 =𝑛𝑛𝜆𝜆4


5th harmonic


What is the fundamental frequency of a pipe that is open at both ends and is 1.715 meters long?

A) 200 HzB) 0.8575 mC) 100 HzD) 3.43 mE) 50 Hz

BA


What is the fundamental frequency of a pipe that is open at both ends and is 1.715 meters long?

A) 200 HzB) 0.8575 mC) 100 HzD) 3.43 mE) 50 Hz

BA

𝑓𝑓1 =𝑣𝑣2𝐿𝐿

=343 m/s

2(1.715 m)= 100 Hz


Assume a flute behaves as a pipe open at both ends. What is the frequency of the third natural mode of a flute with a length of 0.8575 meters?

A) 100 HzB) 200 HzC) 300 HzD) 600 HzE) None of the above

BA


Assume a flute behaves as a pipe open at both ends. What is the frequency of the third natural mode of a flute with a length of 0.8575 meters?

A) 100 HzB) 200 HzC) 300 HzD) 600 HzE) None of the above

BA

𝑓𝑓3 =3𝑣𝑣2𝐿𝐿

=3(343 m/s)2(0.8575 m)

= 600 Hz


A clarinet can be closely approximated as a cylindrical pipe that is closed at one end. What might be the harmonics present for a clarinet (in Hz)?

A) 121, 233, 251, …B) 120, 240, 360, …C) 120, 360, 600, …D) None of the above

BA


A clarinet can be closely approximated as a cylindrical pipe that is closed at one end. What might be the harmonics present for a clarinet (in Hz)?

A) 121, 233, 251, …B) 120, 240, 360, …C) 120, 360, 600, …D) Not enough information to determine

BA

(even harmonics absent)


Demo: Rubens’ tube


• How to change pitch?

• Sound speed (𝑣𝑣)?

• Length (𝐿𝐿)?• valves, tone holes

• Harmonic number (𝑛𝑛)?• overblowing, embouchure


open

𝑓𝑓𝑛𝑛 = 𝑛𝑛𝑣𝑣

4𝐿𝐿(closed)

Types of Aerophones

1. Free: does not contain the vibrating air (no standing waves)• Examples: siren, whip, harmonica,

accordion, bullroarer2. Flute-type: open-open tube; sound

produced from edge tones• Examples: flute, recorder, organ pipe

3. Reed/brass: open-closed tube (cylindrical, conical, or flared bell); sound produced from vibrating reed/lips• Examples: clarinet, saxophone,

trumpet, horn, didgeridoo

https://www.youtube.com/watch?v=2ODGE2f7gLQ

Aerophones

• How to create standing waves in pipes?

1. Edge Tones

2. Reeds

Edge Tones

• Fluid-flow instabilities:“vortex shedding”

• Examples:• Flag fluttering in wind• Seatbelt in fast car• Aeolian harp• Blowing on bottle lip• Whistle

Edge Tones

• Ball whistle: vortex shedding onedge, plus turbulent feedback fromredirected air

• Edge tones: frequency of oscillationincreases with increasing wind speed

Organs

• Two types of pipes: flue pipes, reed pipes

• Console: keyboards, stops

Organs

• Stops: each one controls a different set (“rank” ) of pipes

• Labelled by length of largest pipe (e.g. 8’, 4’, 15/3’)

PresenterPresentation NotesBoardwalk Hall Auditorium Organ, Atlantic City, NJ“Largest musical instrument ever constructed” (33,112 pipes, with the largest measuring 64 ft)“Loudest musical instrument ever constructed” (130 dB)

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Physics 1240: Sound and Music · Physics 1240: Sound and Music. Today (7/25/19): Vibrating Air Columns, Organs. Next time: Woodwinds, Brass Instruments